On the tape, Trump is heard boasting in lewd terms about a failed attempt to seduce a married woman and talks about kissing and groping women without heir consent, saying "when you're a star, they let you do it."

Bush, then an anchor for the entertainment show, is heard on the tape laughing and joking along with Trump.

In his memo Monday, Oppenheim wrote of Bush: "While he was a new member of the TODAY team, he was a valued colleague and longtime member of the broader NBC family. We wish him success as he goes forward."

Bush apologized in a personal statement after the video surfaced, saying: "Obviously I'm embarrassed and ashamed. It's no excuse, but this happened 11 years ago — I was younger, less mature, and acted foolishly in playing along. I'm very sorry."

"Access Hollywood" is owned and distributed by NBCUniversal, the parent company of NBC News and CNBC.